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Recent items include:

  • The Laplace limit
  • Aitken acceleration before Aitken
  • e approximation

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johndcook.com /1 month ago

The Laplace limit

An earlier post discussed how to solve Kepler’s equation M =В E в€’В e sin(E) using a sine series. You could also solve Kepler’s equation using a power series, which Lagrange did i...

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johndcook.com /1 month ago

Aitken acceleration before Aitken

Kepler solved his eponymous equation M =В E в€’В e sin(E) by finding a fixed point of E = M + e sin(E). So guess a value ofВ E and stick it into the right hand side. Then plug that...

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johndcook.com /1 week ago

e approximation

I ran across the approximation e ≈ 2721/1001 recently. What makes this remarkable is its accuracy relative to the size of the denominator. You can create a trivial approxima...

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johndcook.com /1 month ago

Mr. Bessel’s eponymous functions

Yesterday I wrote a post showing that the trapezoid rule evaluates the integral very efficiently. But how do we know what the exact integral is for comparison? If you ask Mathemati...

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johndcook.com /3 weeks ago

Lobachevsky’s integral formula

Let f be an even function with period ПЂ. Then the following remarkable theorem by Lobachevsky holds. This theorem is useful in Fourier analysis and signal processing. It’s useful...

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